8 papers
Hamilton--Jacobi theory for non-conservative field theories in the -contact framework
Javier de Lucas, Julia Lange, Xavier Rivas +1
This article develops a Hamilton--Jacobi theory for non-conservative classical field theories, with particular emphasis on dissipative systems, in the framework of co-oriented k-co…
Noether-Type Theorems and the Generalized Herglotz Principle in -Contact Geometry
Melvin Leok, Cristina Sardón, Xuefeng Zhao
We develop a unified geometric framework for dissipative mechanical systems based on uniform -contact manifolds, which provide an extended phase space equipped with multiple con…
Exact integration of Hamiltonian dynamics via Jacobi and Poisson Cinf-structures
A. J. Pan-Collantes, C. Sardón, X. Zhao
We develop a geometric framework for the exact integration of Hamiltonian systems based on triangular closure relations among a finite family of functions. Unlike Liouville-Arnold…
Symmetries and Weighted Integrability of Vector Fields with Jacobi Multipliers
C. Sardón, X. Zhao
In this paper, we investigate analytic divergence-free vector fields and vector fields admitting a Jacobi multiplier on -dimensional Riemannian manifolds. We first introduce a f…
(Quasi) Hamiltonian Systems and Non-Decomposable Poisson Geometry
C. Sardón, X. Zhao
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the…
From Dirac to Dunkl Operators through Symmetry Reduction
Cristina Sardón
This paper presents a geometric and analytic derivation of Dirac-Dunkl operators as symmetry reductions of the flat Dirac operator on Euclidean space. Starting from the standard Di…